The van der Waals interaction between two ground-state atoms is calculated for two electrically or magnetically polarizable particles embedded in a dispersive magnetodielectric medium. Unlike previous calculations which infer the atom-atom interaction from the dilute-medium limit of the macroscopic, many-body van der Waals interaction, the interaction is calculated directly for the system of two atoms in a magnetodielectric medium. Two approaches are presented, the first based on the quantized electromagnetic field in a dispersive medium without absorption and the second on Green functions that allow for absorption. We show that the correct van der Waals interactions are obtained regardless of whether absorption in the host medium is explicitly taken into account.

We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimization problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimization corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.

We consider interactions that generate a universal set of quantum gates on logical qubits encoded in a collective-dephasing-free subspace, and discuss their implementations with trapped ions. This allows for the removal of the by-far largest source of decoherence in current trapped-ion experiments, collective dephasing. In addition, an explicit parametrization of all two-body Hamiltonians able to generate such gates without the system’s state ever exiting the protected subspace is provided.

The time evolution of spin states of two electrons interacting with a nuclear spin bath in a quantum dot system is studied. The hyperfine interaction between the electrons and the nuclear spins is modeled by an isotropic Heisenberg interaction, and the interaction between the electron spins by Heisenberg exchange. Depending on the extent of the overlap between the spatial wave functions of the electrons, there are two physically different cases, namely, the two qubits either interact with the same set of nuclear spins or they see different nuclear spin environments. In the two cases, the decoherence of the two-qubit state is studied analytically. We have identified a class of two-qubit states that have a rich dynamics when the exchange interaction between the qubits becomes large in comparison to the hyperfine interaction strengths. The decoherence time scale is determined as a function of the bath-spin distribution and the polarizations of the initial two-qubit state. States with large decoherence times are identified by performing a minimization over all the two-qubit pure states.

We model an optical implementation of a controlled-SIGN gate that makes use of the quantum Zeno effect [Franson et al., Phys. Rev. A 70, 062302 (2004)] in the presence of photon loss. Gate operation is severely affected. However, we show that by using photon loss codes proposed for linear optical quantum computation (LOQC), performance is greatly enhanced, outperforming LOQC equivalents. The technique can be applied to other types of nonlinearities, making the implementation of nonlinear optical gates much more attractive.

Variational calculations employing explicitly correlated Gaussian functions have been performed for the ground states of ${}^9\mathrm{Be}$ and ${}^9\mathrm{Be}^{+}$ including the nuclear motion [i.e., without assuming the Born-Oppenheimer (BO) approximation]. An approach based on the analytical energy gradient calculated with respect to the Gaussian exponential parameters was employed, leading to energies of the two systems noticeably improved over those found in the recent paper of Pachucki and Komasa [Phys. Rev. A 73, 052502 (2006)]. The non-BO wave functions were used to calculate the ${\alpha }^2$ relativistic corrections $(\alpha =e^2∕\hslash c)$. With those corrections and the ${\alpha }^3$ and ${\alpha }^4$ corrections taken from Pachucki and Komasa, a new value of the ionization potential (IP) of ${}^9\mathrm{Be}$ was determined. It agrees very well with the most recent experimental IP.

Absolute total electron-trimethylamine scattering cross section (TCS) has been measured from $0.8\text{to}370\mathrm{eV}$ with a linear electron-transmission method. The experimental TCS energy function is dominated by very pronounced enhancement peaked near $9\mathrm{eV}$. The present TCS agrees qualitatively with low-energy results of Schmieder [Z. Elektrochem. 36, 700 (1930)] but there are substantial differences in the position and peak values. Calculations were also carried out to obtain the integral elastic and ionization cross sections at intermediate and high energies using the independent atom (IAM) and the binary-encounter-Bethe (BEB) approximations, respectively. Their sum, the estimated total cross section, is for intermediate energies in a reasonable agreement with the present experimental TCS data. Furthermore, the measured TCS for $\mathrm{N}{\left(\mathrm{C}{\mathrm{H}}_3\right)}_3$ is compared with the TCSs for other nitrous compounds: $\mathrm{N}{\mathrm{H}}_3$ and $\mathrm{N}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$. The variation of the TCS magnitude across the series of nitrogen-containing molecules [$\mathrm{N}{\mathrm{H}}_3$, $\mathrm{N}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_3$, and $\mathrm{N}{\left(\mathrm{C}{\mathrm{H}}_3\right)}_3$] is explained in terms of their molecular size.

In a recent work we compared spin-free collisions of $\mathrm{N}_2{}^{+}$ with ${}^3\mathrm{He}$ and ${}^4\mathrm{He}$ using a newly developed potential energy surface. We found that such collisions exhibit a strong isotope effect in the ultracold regime. In the present study we consider the role of the spin-rotation interaction in cold $\mathrm{He}\text{−}\mathrm{N}_2{}^{+}$ collisions. We find that our spin-free vibrational quenching cross sections are not affected. Conversely, the cross sections for rotational quenching are strongly modified in the ultracold regime and exhibit resonance structures which are analyzed. These structures, which are not observed when the spin-rotation interaction is omitted, are shown to be due to the Feshbach resonances associated with the nonconservation of parity.

In many experiments involving a magneto-optical trap (MOT) it is of great importance to know the fraction of atoms placed in an excited state due to the trapping process. Generally speaking, researchers have had to use overly simplistic and untested models to estimate this fraction. In this work, the excited fractions of ${}^{87}\mathrm{Rb}$ atoms in a MOT are directly measured using a charge transfer technique, for a range of MOT parameters. Simple models are then fit to the measured fractions. Using the results of this work, the excited fraction of ${}^{87}\mathrm{Rb}$ atoms trapped in a MOT can be accurately estimated with knowledge of only the trapping laser intensity and detuning. The results are, at most, only weakly dependent on other MOT parameters.

A dense Bose gas with hard-core interaction is considered in an optical lattice. We study the phase diagram in terms of a special mean-field theory that describes a Bose-Einstein condensate and a Mott insulator with a single particle per lattice site for zero as well as for nonzero temperatures. We calculate the densities, the excitation spectrum, and the static structure factor for each of these phases.

We observe quantum beats with periodic revivals due to nonlinear spacing of Zeeman levels in the ground state of potassium atoms, and demonstrate their synchronous optical pumping by double modulation of the pumping light at the Larmor frequency and the revival frequency. We show that synchronous pumping increases the degree of spin polarization by a factor of 4. As a practical example, we explore the application of this double-modulation technique to atomic magnetometers operating in the geomagnetic field range, and find that it can increase the sensitivity and reduce magnetic-field-orientation-dependent measurement errors endemic to alkali-metal magnetometers.

The Einstein-Podolsky-Rosen (EPR) argument revealed the paradoxical properties of a two-particle system entangled continuously in the spatial parameter. Yet a direct test of quantum nonlocality exhibited by this state, via a violation of Bell’s inequality, has not been forthcoming. In this paper, we identify and construct experimental arrangements comprising simple optical components, without nonlinearities or moving parts, that implement operators in the spatial-parity space of single-photon fields that correspond to the familiar Pauli spin operators. We achieve this by first establishing an isomorphism between the single-mode multiphoton electromagnetic-field space spanned by a Fock-state basis and the single-photon multimode electromagnetic-field space spanned by a spatial-eigenmode basis. We then proceed to construct a Hilbert space with a two-dimensional basis of spatial even-odd parity modes. In particular, we describe an arrangement that implements a rotation in the parity space of each photon of an entangled-photon pair, allowing for a straightforward experimental test of Bell’s inequality using the EPR state. Finally, the violation of a Bell inequality is quantified in terms of the physical parameters of the two-photon source.

The use of Rényi entropy as an uncertainty measure alternative to variance leads to the study of states with quantum fluctuations below the levels established by Gaussian states, which are the position-momentum minimum uncertainty states according to variance. We examine the quantum properties of states with exponential wave functions, which combine reduced fluctuations with practical feasibility.

We give a scheme for a physical implementation of the programmable state discriminator that unambiguously discriminates between two unknown qubit states with optimal probability of success. One copy of each of the unknown states is provided as input, or program, for the two program registers, and the data state, which is guaranteed to be prepared in one of the program states, is fed into the data register of the device. This device will then tell us, in an optimal way, which of the templates stored in the program registers the data state matches. The implementation is based on Neumark’s theorem. We introduce a single qubit as ancilla and a unitary operator that entangles the system with the ancilla in such a way that projective measurements performed in the computational basis of the system plus ancilla transform the initial system states according to the optimal positive-operator-valued measure.

Core shell excitation spectra of aniline at the carbon and nitrogen $1s$ edges have been obtained by inner-shell electron energy-loss spectroscopy recorded under scattering conditions where electric dipolar conditions dominate, with higher resolution than in the previous studies. They are interpreted with the aid of ab initio configuration interaction calculations. The spectrum at the C $1s$ edge is dominated by an intense ${\pi }^{*}$ band. The calculated chemical shift due to the different chemical environment at the carbon $1s$ edge calculated is in agreement with the experimental observations within a few tenths of an eV. The transition energies of the most intense bands in the C $1s$ excitation spectrum are discussed at different levels of calculations. In the nitrogen $1s$ excitation spectrum the most intense bands are due to Rydberg-valence transitions involving the ${\sigma }^{*}$-type molecular orbitals, in agreement with the experiment. This assignment is different from that of extended Hückel molecular orbital calculations. The geometries of the core excited states have been calculated and compared to their equivalent core molecules and benzene.

Results of theoretical calculations of ionization rates of Rb and Na Rydberg atoms by blackbody radiation (BBR) are presented. Calculations have been performed for $nS$, $nP$, and $nD$ states of Na and Rb, which are commonly used in a variety of experiments, at principal quantum numbers $n=8–65$ and at three ambient temperatures of 77, 300, and $600\mathrm{K}$. A peculiarity of our calculations is that we take into account the contributions of BBR-induced redistribution of population between Rydberg states prior to photoionization and field ionization by extraction electric field pulses. The obtained results show that these phenomena affect both the magnitude of measured ionization rates and shapes of their dependences on $n$. The calculated ionization rates are compared with the results of our earlier measurements of BBR-induced ionization rates of Na $nS$ and $nD$ Rydberg states with $n=8–20$ at $300\mathrm{K}$. A good agreement for all states except $nS$ with $n>15$ is observed. We also present the useful analytical formulas for the quick estimation of BBR ionization rates of Rydberg atoms.

Spontaneous emission of an atom (molecule) placed near a nanocylinder of elliptical cross section of an arbitrary composition is studied. The analytical expressions have been obtained for the radiative and nonradiative rates of spontaneous decay and investigated in details.

A two-level system that is coupled to a high-finesse cavity in the Purcell regime exhibits a giant optical nonlinearity due to the saturation of the two-level system at very low intensities, of the order of one photon per lifetime. We perform a detailed analysis of this effect, taking into account the most important practical imperfections. Our conclusion is that an experimental demonstration of the giant nonlinearity is feasible using semiconductor micropillar cavities containing a single quantum dot in resonance with the cavity mode.